Proceedings Template - WORDTime Series based Air Pollution Forecasting using SARIMA and Prophet Model
K. Krishna Rani Samal Korra Sathya Babu Santosh Kumar Das Abhirup Acharaya
Department of CSE
NIT Rourkela, India.
Mob: +91 9874641997
Department of CSE
NIT Rourkela, India.
Mob: +91 8249892662
Department of ECE
NIT Rourkela, India
Mob: +91 9437940105
Department of ECE
NIT Rourkela, India
ABSTRACT
Air pollution severely affects many countries around the world
causing serious health effects or death. Increasing dependency on
fossil fuels through the last century has been responsible for the
degradation in our atmospheric condition. Pollution emitting from
various vehicles also cause an immense amount of pollution.
Pollutants like RSPM, SO2, NO2, SPM, etc. are the major
contributors to air pollution which can lead to acute and chronic
effects on human health. The research focus of this paper is to
identify the usefulness of analytics models to build a system that is
capable of giving a rough estimate of the future levels of pollution
within a considerable confidence interval. Rendered linear
regression techniques are found to be insufficient for the time-
dependent data. In this regard, we have used time series forecasting
approach for predicting the future levels of various pollutants
within a considerable confidence interval. The experimental
analysis of the forecasting for the air pollution levels of
Bhubaneswar City indicates the effectiveness of our
proposed method using SARIMA and Prophet model.
CCS Concepts
General programming languages
“SO2”, “NO2”, “RSPM”, “SPM”
1. INTRODUCTION Human population growth is becoming a tensed issue and this
overpopulation has brought many undesirable effects on the
environment. Many social and economic factors are having a very
bad influence on the environment. The results of this harmful
influence lead to the release of hazardous pollutants such as SO2,
NO2, RSPM, SPM, etc. into the atmosphere. Prolonged to such
particles can cause several acute as well as chronic health issues.
Every day around 93 percent of the world’s children suffer from
environmental health risk due to air pollution. Odisha health care
data is analyzed to evaluate the health effects of pollutants and
concluded that 4.80 percentage of death occurred per 100000
populations in Odisha during 2014 is due to respiratory diseases as
shown in Figure 1.
Figure 1. Percentage of death due to respiratory syndrome
The air pollution has become so severe that the public should be
timely informed about pollution level and environmental changes
so that they can be cautious to keep them safe. Therefore, there
are many forecasting models being in use to predict the pollution
level in advance, however there is still a requirement of a more
accurate mathematical model to forecast the pollution level and air
quality index, which has the negative impact on human health. Air
pollution level turns so severe in India [1] so that this has become
a leading factor of cancer, heart diseases, cancer, many respiratory
infections. Exposure to NO2, SPM can affect our lungs and
respiratory system, hence the effects of air pollution are alarming
[2]. In that case, everyone has to be alerted regarding this danger
sign. Due to government economic budget, it is very difficult to
deploy efficient sensors at everywhere to measure the pollution
levels to alert the public in advance. Therefore, it is better to
develop a model which can forecast pollution level in advance
without the direct use of any sensors in real time [3].
2. RELATED WORKS Principle component analysis technique is used to forecast the
pollutant value in one-day advance [1]. It also works well, when
there is a large number of data with the belief that some variables
are correlated to each other. During the model evaluation, it is
found that it performs well in the winter season than the other
seasons. The author of the paper [3] represents a health advisory
model using Big data analytics technologies, which can alert people
about the health effect of rising in single-pollutant level as well as
a mixture of many such pollutants. This proposed model is also
efficient to solve sparse data issues and overcome the barrier of the
single numerical model by providing ensemble estimation
technique. The author analyzed health care data and estimated
individual air quality health risk factor for protecting their health.
Paper [4] presents an ensemble learning method and multi-channel
ensemble learning via supervised assignment. It is difficult to
monitor the pollution level at each point of the area, so the author
has proposed MELSA algorithm for forecasting pollution quality
and uses web service to deliver predictive analytic results to various
stakeholders. The author of paper [5] made practical and efficient
use of Linear regression and multilayer perceptron to understand
the pattern and depth of pollution level. In the paper [6], the author
found that SO2, NO2 are also important factors for the increasing
level of PM2.5. In this paper, the author proposed a genetic
algorithm optimization BP neural to forecast PM2.5 value but still
it has some disadvantage like it requires many parameters to work
with and range can be given by experience. In [7] the author utilized
univariate modeling for concentration value of one gas. The author
presents Multivariate modeling, while different features are
including such as temporal features, meteorological features. Paper
[7] utilizes ANN, SVM and provided a conclusion that ANN is not
very useful for a small data set, having many attributes due to its
poor generalization. SVM works well due to its ability to
implement high dimensionality data. Yuchao Zhou et.al [8]
proposed NARX predictive model to forecast air quality index. The
author also concluded his study with the words that the neural
network does not perform well for PM10 data. In the paper [9]
author proposed hybrid PLS-SVM algorithm to provide an
alternative to time series forecasting but the author has considered
only CO value to develop the daily and hourly prediction model.
Here, a comparative study has been done between SVM and PLS-
SVM and concluded that PLS-SVM provides more accuracy in
terms of RMSE value. Nam-UK Lee et al. [10] proposed an
algorithm seasonal autoregressive integrated moving average-
support vector machine (SARIMA-SVM) which can analyze both
seasonality and non-linear characteristics. D.S. Voynikova et al.
[11] implemented SARIMA model to analyze the most problematic
S02 and PM10 pollutant values using five meteorological variables
as tools and concluded that air temperature, wind speed, pressure,
and humidity have a high influence on the rise of pollutant concentration level. Mihaela et al. [12] implemented artificial
neural network(ANN) and adaptive neuro-fuzzy inference
systems(ANFIS) to forecast PM2.5 value and compared the
accuracy of both the models, then arrived at the opinion that ANN
model is better than ANFIS for PM2.5 value forecasting. Nur
haizum abd Rahman et al. [13] studied the correlation between
pollution and its impact on human health by utilizing both classical
and modern approach, specifically SARIMA and fuzzy time
series(FTS) method. However, these models were able to give good
accuracy during AQI value forecasting. Shalini and Mandowara in
paper [14] studied Particulate Matter Pollution in Jaipur City and
concluded that PM2.5 and PM10 decrease in monsoon, increase in
winter and summer season gradually. In this paper, the author
implemented the ARIMA model and considered only seasonal
effects on pollution level but not the impact of holidays on the rise
of pollution level. Air pollution level gets worse during holidays
like Diwali. Hence, we tried to improve the existing work by
considering the impact of holidays and seasonal effect on air quality
level with the implementation of SARIMA model and Prophet
model and compared the results to identify the most successful
model for air quality forecasting.
3. PROBLEM STATEMENT Air pollution is an alarming problem for the globe, specifically it is
a more challenging problem for developing countries like India.
This is because India needs faster sustainable development.
Continuous measurement and monitoring of air pollution levels
across the cities are required to effectively manage this issue. It is
essential for policymakers to predict the pollutant levels specific to
particular geolocation by analyzing the hidden trends available in
the managed historical pollution data. Hence, in our research our
prime objective is to estimate the increasing level of air pollution
of Bhubaneswar city using a historical data set of the parameters
measured and to forecast their values after a specific time interval.
Further, there is a need for time series forecasting by machine
learning algorithms to accomplishing it. This forecasting
methodology can give forecast value periodically to effectively
manage air pollution problems.
4. MATERIALS AND METHODOLOGIES
4.1 Research Location
Bhubaneswar being capital of Odisha is one of the smartest city in
state. The latitude of Bhubaneswar, India is 20.296059, and
longitude is 85. 824539. Bhubaneswar city is located in India and
is placed in city category with the GPS coordinates of 20 17
45.8124 N and 85 49 28.3404 E. Open source air pollution
historical data [15] of capital police stations, Bhubaneswar is
considered as source data for this research. Figure 2 with dotted
symbols represent all the air pollution monitoring stations of
Odisha.
4.2 Methods The present paper implemented Box-Jenkins model and prophet
model to identify the most effective pollution forecasting model.
Box-Jenkins model: Box-Jenkins model is a mathematical model
and is also used for time series forecasting [16] based on auto
regression (AR), differencing and moving average (MA). The
model can be treated as univariate time series forecasting model. It
first checks for stationarity and seasonality, then identifies AR, MA
parameter. It follows the differencing process to convert non
stationarity data to stationary, which generates the ARIMA (Auto
regressive integrated moving average) model.
ARIMA model can be used for both data generation and
forecasting [16] [17]. General notation follows for an ARIMA
model is ARIMA (p; d; q), where p is the number of auto regressive
terms, d is the order of differencing, q is the number of moving
average terms. This model can be used for non-stationary data.
Presence of non-stationary can be checked by various statistical
method. Differencing is one of the methods. First, it applies
differencing to make the series of data stationary and then apply the
ARIMA model. After differencing steps, it finds out AR, MA
parameters then it uses a particular model [18]. ARIMA has two
different types of models based on the seasonal effects, such as
ARIMA and SARIMA model. Seasonal ARIMA can be used to
forecast the values during special holidays [19]. The generalized
form of the ARIMA model is given in Equation 1,
1 1
L L X L
i is the moving average part parameter
t is the error term.
SARIMA (Seasonal auto regressive integrated moving average)
model is similar to the ARIMA model but this model is preferable
when the time series exhibits seasonality. Mathematically it can be
expressed in terms of a composite model which can be denoted as
( , , )( , , )ARIMA p d q P D Q S . Here, the model parameters p, d and
q represent the non-seasonal AR order, no seasonal differencing,
non-seasonal MA order respectively. Further, the model parameters
P , D , Q and S are corresponding to the seasonal AR order,
seasonal differencing, seasonal MA order, and time span of
repeating seasonal pattern respectively. However, the model can be
further expressed in simple form without differencing part as
mentioned in Equation 2 [16], [20].
( ) ( )(1 ) (1 ) ( ) ( ) s d s D s
B B B B Y B Bp p t q tQ (2)
where,
S S PS B B B Bp P
q q qB B B B
Q Q QSS S
Prophet forecasting Model: This model is developed by
Facebook, available in python and R [21] [22]. Due to its
three main features, ie. trend, seasonality, holidays [23] and
demand for the high quality of forecasting are the main reason for
building this model. It can be represented as in Equation 3,
( ) g( )+s( ) h( )y t t t t t (3)
where the model parameters g( )t , s( )t , h( )t , t are piecewise
linear curve for modeling non-periodic changes in time series,
periodic changes, the effects of holidays with irregular schedules,
error term accounts for any unusual changes not accommodated by
the model respectively. To fit the proposed model with seasonality
effects and forecast based on it, it uses a Fourier series which
provides a flexible model. Seasonal effects s( )t can be represented
as in Equation 4 [24],
2 2 ( ) cos( ) sin( )

where, p represents regular period
5. MEASURE OF ACCURACY RMSE and MSE are the two criteria chosen to measure the
performance of time series forecasting model as shown in Equation
5 and Equation 6 where error is , = 0,1,2,3,… . The model
which is having the least value of RMSE and MSE is selected as
the best pollution forecasting model.
21RMSE : 1
n en i
i
(6)
6. RESULTS AND DISCUSSIONS In this part, we present the time series pollution forecasting using
historical pollution dataset of Bhubaneswar city, India. The
analyzed data included year wise data from 2005 to 2015. The
dataset contains pollutant values i.e. SO2, NO2, SPM, RSPM
values with GPS coordinate for various pollution monitoring
stations of Odisha, India. The data is processed according to the
requirement of the forecasting model and missing values are
tackled using mode void fill method, using backward and forward
fill wherever deemed fit and necessary.
The time series plots illustrate that there is roughly a constant level
of certain pollutants. In addition to that, there is also a constant level
of seasonal fluctuation and random fluctuations over time.
Differencing process is done to handle this type of situation before
forecasting model development. The weekly, monthly and yearly
seasonality checked. The required parameters also fed to the model
for a more precise forecast. The Indian holiday list feed is expected
to significantly boost the model performance as it would add an
extra parameter for better correlation amongst the dates and the
pollutant levels correspondingly. There are three main steps i.e.
stationary test, model identification, and forecasting in building the
forecasting model.
6.1 Stationary Test The present paper implemented Dickey-Fuller test to check the
stationarity of the data before the SARIMA and prophet model
implementation. Results of dickey fuller test that conducted year
wise for each pollutant are shown in Figure 3 - Figure 6. In
summary, we concluded from this test that the test statistics is less
than the p-value for each time series pollutant value which implies
that series are not stationary. Log transformation is also used to
stabilize the non-constant variance of time series.
Figure 3. Dickey-Fuller test for SPM
Figure 4. Dickey-Fuller test for NO2
Figure 5. Dickey-Fuller test for SO2
Figure 6. Dickey-Fuller test for RSPM
6.2 Model Identification Akaike Information Criteria (AIC) and Bayesian information
criterion(BIC) are two statistical measure of SARIMA model [25].
The model with lower AIC and BIC value is better while comparing
two models. Hence, the combination of these measure is used to
identify the best order of the SARIMA model for pollution
forecasting. Table 1 shows the lower value of these measure which
considered to select the best order of the SARIMA model for each
pollutant.
Table 1: AIC and BIC values to find the best order of
SARIMA model
Pollutant SPM NO2 SO2 RSPM
Order (0,1,2) (0, 1, 2) (0, 1, 2) (1, 1, 1)
Seasonal
order
AIC 20.157 20.157 -1244.481 552.886
BIC 45.691 45.691 -1233.532 578.421
6.3 Forecasting using SARIMA and Prophet Model Log transformation is used in this paper while developing a
forecasting model to convert nonstationary time series into a
stationary time series to achieve better performance. The actual
results and forecasting results of SARIMA model are shown in
Figure 7 - Figure 10. The actual results and predicted results of
time series Prophet on log model are shown in Figure 11 - Figure
14.
Figure 11. Prophet on log model-SPM
Figure 12. Prophet on log model-NO2
Figure 12: Prophet on log model-SO2
Figure 14. Prophet on log model-RSPM
7. COMPARATIVE ANALYSIS The predictions of air pollution level are location dependent.
Further, there is no previous reported work of prediction of air
pollution levels corresponding to our research location, i.e.
Bhubaneswar. However, similar types of techniques are applied to
one of the cities of Bulgaria [11]. Hence, comparison is made
between the general and logarithmic models to identify the
successful model for forecasting. The experimental results show
that logarithmic model works better at adapting to the long term
trends and anomalies in the pollutant levels. The results show that
the log-model gives comparatively slightly better values as
compared to the general model on a larger scale. Comparison of
performance metrics for SARIMA Model and Prophet Model are
shown in Table 2-Table 4.
Table 2- Accuracy Metrics for SARIMA general model
Metric/Pollutant SPM NO2 SO2 RSPM
RMSE 4.13 4.13 2.55 57.04
MSE 17.12 17.12 6.50 3254.158
Table 3. Accuracy Metrics for Prophet general model
Metric/Pollutant SPM NO2 SO2 RSPM
RMSE 3.78 3.57 2.15 45.80
MSE 14.34 12.75 4.65 2097.77
Table 4. Accuracy Metrics for Prophet log model
Metric/Pollutant SPM NO2 SO2 RSPM
RMSE 3.54 3.54 2.141 39.86
MSE 12.55 12.55 4.58 1589.259
We have also compared the performance of Prophet general model
and Prophet log model using their performance metric and
concluded that prophet log model provides more accurate
forecasting results than Prophet general model.
8. CONCLUSION In this work, we have proposed two approaches for pollution
forecasting based on the historical data which contains information
from 2005 to 2015. The proposed model predicted pollutant value
for 2016. We made a comparison between the model’s performance
metrics. By looking into the accuracy metric values in Table 2-
Table 4, we conclude that both the SARIMA and prophet model
provides a good quality of accuracy. However, the best approach is
the prophet model on log transformation which has the least
minimum RMSE, MSE value. The results show the feasibility of
using time series forecasting model, i.e. Prophet model to forecast
the future level of pollution and build an early warning system for
public safety. This work can be extended by analyzing health care
data to establish health correlation with the pollution level in the
future. However, due to the lack of recent data availability, we have
restricted our research to the year 2015. Further, the proposed
method can be enhanced using a deep learning algorithm to achieve
a much higher degree of freedom, versatility, adaptability, and
accuracy.
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Authors’ background Your Name Title* Research Field Personal website
K.Krishna Rani Samal Ph.D. Student Analytics http://isdr.nitrkl.ac.in/team.html
Dr. Korra Sathya Babu Assistant Professor Analytics, Natural Language
Processing https://www.nitrkl.ac.in/CS/~ksathyababu/
Dr. Santos Kumar Das Assistant Professor Optical networking and embedded
IoT system https://www.nitrkl.ac.in/EC/~dassk/